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Some comments on
"Estimating the extent of price stickiness in Hungary:
a hazard-based approach"
P. GABRIEL & A. REIFF
P. Sevestre
Motivation
Most of the recently provided estimates of the average durationof price spells considered to be an indicator of price stickinessare biased estimates of the relevant mean duration.
The relevant average is indeed that of the distribution of theduration of uncensored spells considered across firms/outletsbut not across spells themselves: there is anover-representation of short spells in the latter, not in the former.
The difference appears to be very important: the resultsprovided in the paper show that the "good" estimates are aboutthe double of the "incorrect" ones as they have been obtained inprevious studies (e.g. the IPN).
If this assertion is valid, this is likely to lead to strong revisions inour assessment of price rigidities (leaving aside the issue ofwhether long durations are necessarily an indicator of strongnominal rigidities.).
The main issue: the over-representation of short spells:
|—|—|—|—|—| 5 uncensored spells - this paper: use a combination of statistics related to: - the distribution of ages, i.e. the elapsed duration of all (right censored) spells, at a given point in time, - the dist. of durations, i.e. the ex-post observed duration, of uncensored spells that are on-going at a given point in time, - the estimated hazards (cf. Dixon).
- Dias et al., Fougere et al., others : sample one spell perfirm/outlet.
- Baharad and Eden : spell weight is proportional to durations - Baudry et al. and others : spell weight is proportional to theinverse of the number of spells in the category.
NB These last two ways of reweighting each spell areequivalent if the price trajectories are of equal length, i.e. are notcorrelated with the duration of spells |—|—|—|—|—| 5 uncensored spells |———————| 1 uncensored spell  weighting with durations leads here to an over-weighting oflong spells. On French data, there is a positive and significantcorrelation between the length of spells and that of thetrajectories: shorter spells do not compensate by their number!!! Indeed, the results strongly differ in practice: to 14 months (duration weights) in France; to 16 months (Dixon’s methodology) in this paper.
Exercise 1: Average length of uncensored spells in a sample where
only one spell per firm
/outlet is kept (cf. Fougere et al.):
This leads to a duration that remains about 7 months for Frenchdata. But this is true that trajectories with a unique long (often)censored spell are excluded. This tends to lower the estimatedmean duration.
"Exercise" 2: using frequencies: This leads to an estimate slightly
above 8 months for France
.
I do not agree with the statement saying that "in case of thecross-sectional age distribution, a long spell. has much higherchance to be sampled". Because the (short) spells are repeated.
In particular, in the situation where all trajectories have thesame length, there is no difference.
|—|—|—|—|—| 5 uncensored spells However, some bias may indeed occur because as longerspells are associated with longer price trajectories  they arelikely more to be sampled than short spells but. this bias wouldnot exist when product/outlet replacements with similarcharacteristics occur.
Which estimates should we retain?
- what are the underlying assumptions? Are they likely to besatisfied? - stationarity (constancy) of the frequency of price changes - homogeneity/heterogeneity of the population (?) - The correction suggested is quite strong. Getting a "correct"average duration of 16 months (14 months in France) which isthe double of the other estimates seems surprising.
Let’s leave aside the econometric issues and look at theplausibility of the estimates: - The estimated average duration for clothing and footwear - it is about 7 months for unprocessed food.
- Why do you consider a decreasing hazard for your example? - You say in a footnote (page 19) that leaving the sales in thesample leads to longer estimated durations.

Source: http://www.francescobilli.it/rcfea.org.1.0/discussant/Discussion%20by%20Sevestre%20of%20Reif.pdf

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